Gauss-Seidel method not converging/throwing error?

I wrote a code for the Gauss-Seidel iterative method. I need to use the method to solve two different systems. For system 1, the code works perfectly. For system 2, I get the following error:

Warning: Rank deficient, rank = 0, tol = NaN. 
> In gauss2 at 10

and then it has Inf then NaN for some of entries in the output matrix. Can anyone tell me why this is happening?! I also attached the matrices. Here's my code.

function F=gauss2(A,b,x0,tol,imax)

B=length(b);
x=zeros(length(b),1);

for j=1:imax
  for k=1:B
      x(k)=1/A(k,k)*(-A(k,1:k-1)*x(1:k-1)-A(k,k+1:B)*x0(k+1:B)+b(k));
  end
      if all(abs((x-x0)./x))<tol;
      break
  else
      x0=x;
      end
end
soln=x         
end

Answer 1

[John D'Errico]

Is x a vector? (Yes. I know it is. I want you to think about the implications of that fact.)

What do you think this test as you wrote it does, when x and x0 are vectors?

if abs((x-x0)/x)<tol

You want to learn about the difference between / and ./, for that read

help slash
doc slash

I think you wanted to use element-wise division (i.e., ./), not the slash (/) that uses linear algebra.

Finally, you need to consider why this test did what it did:

if 0 == [2 0 1]
  disp('they sky is falling') 
else
  disp('all is good in the world')
end

The result will be:

all is good in the world

Since one of the elements in that vector WAS identically zero, the first brach should have been taken, or NOT? Why not?

An if statement, when applied to a vector like that, uses only the very first element of that vector. If you want to test if all of any of the elements of the vector are true, then you need to use the functions ALL or ANY. For example, write it like this:

if any(0 == [2 0 1])
  disp('they sky is falling') 
else
  disp('all is good in the world')
end

Now the first branch will execute because at least ONE of the elements tested to be zero.

help all
help any

Finally, as for your actual question, as to why inf or nan is occurring at line 21, your function does not actually have 21 lines in it. So you have not even given us the function you are actually calling. The crystal ball is so foggy on that question, since I cannot read your mind.

[tess marconie]

Oops, it says line 21 because I deleted some lines at the beginning such as my name and some other comments. It should say line 10, but that is exactly the line you mentioned in your response! Let you know if I get it to work.

[tess marconie]

Yeah, I understand what you are saying in this reply, but it isn't making the code work for the second of system